1 | /* e_acoshl.c -- long double version of e_acosh.c. |
2 | * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. |
3 | */ |
4 | |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | /* __ieee754_acoshl(x) |
17 | * Method : |
18 | * Based on |
19 | * acoshl(x) = logl [ x + sqrtl(x*x-1) ] |
20 | * we have |
21 | * acoshl(x) := logl(x)+ln2, if x is large; else |
22 | * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else |
23 | * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. |
24 | * |
25 | * Special cases: |
26 | * acoshl(x) is NaN with signal if x<1. |
27 | * acoshl(NaN) is NaN without signal. |
28 | */ |
29 | |
30 | #include <math.h> |
31 | #include <math_private.h> |
32 | #include <libm-alias-finite.h> |
33 | |
34 | static const _Float128 |
35 | one = 1.0, |
36 | ln2 = L(0.6931471805599453094172321214581766); |
37 | |
38 | _Float128 |
39 | __ieee754_acoshl(_Float128 x) |
40 | { |
41 | _Float128 t; |
42 | uint64_t lx; |
43 | int64_t hx; |
44 | GET_LDOUBLE_WORDS64(hx,lx,x); |
45 | if(hx<0x3fff000000000000LL) { /* x < 1 */ |
46 | return (x-x)/(x-x); |
47 | } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */ |
48 | if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ |
49 | return x+x; |
50 | } else |
51 | return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ |
52 | } else if(((hx-0x3fff000000000000LL)|lx)==0) { |
53 | return 0; /* acosh(1) = 0 */ |
54 | } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ |
55 | t=x*x; |
56 | return __ieee754_logl(2*x-one/(x+sqrtl(t-one))); |
57 | } else { /* 1<x<2 */ |
58 | t = x-one; |
59 | return __log1pl(t+sqrtl(2*t+t*t)); |
60 | } |
61 | } |
62 | libm_alias_finite (__ieee754_acoshl, __acoshl) |
63 | |